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Unbiased forward rate and time horizon in emerging

economies and implications to hedging practices

Finance Master's thesis Veli-Rasmus Varetsalo 2014 Department of Finance Aalto University School of Business Powered by TCPDF (www.tcpdf.org)

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Unbiased forward rate and time horizon in emerging economies and

implications to hedging practices

Finance Master’s Thesis Veli-Rasmus Varetsalo 2014 Department of Finance Aalto University School of Business

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Unbiased forward rate and time

horizon in emerging economies and

implications to hedging practices

Master’s Thesis

Veli-Rasmus Varetsalo

Fall 2014

Finance

Approved in the Department of Finance __ / __20__ and awarded the grade

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Aalto University, P.O. BOX 11000, 00076 AALTO www.aalto.fi Abstract of master’s thesis

Author Veli-Rasmus Varetsalo

Title of thesis Unbiased forward rate and time horizon in emerging economies and implications to hedging practices

Degree Master of Science in Economics and Business Administration Degree programme Finance

Thesis advisor Professor Markku Kaustia

Year of approval 2014 Number of pages 75 Language English

Abstract

PURPOSE OF THE STUDY

The purpose of this study is to test the unbiased forward rate hypothesis in emerging economies and the impact of time horizon. The unbiased forward rate hypothesis tests whether a forward rate is an unbiased predictor of future exchange rate. The implications of findings on hedging foreign exchange risk are intended to be analyzed.

DATA AND METHODOLOGY

The data consists of monthly observations of exchange rates and forward premiums for the maturities of 1-, 3-, 6- and 12-months for ten emerging economies: Brazil, Chile, Czech Republic, India, Indonesia, Mexico, Russia, South Africa, South Korea and Turkey. The exchange rate data is retrieved from Bloomberg terminal and all the quotes are against US dollar. For the aforementioned maturities, the unbiased forward rate hypothesis is tested with the Fama regression model using Newey-West standard errors. The time horizon effect for maturities of one and five years is examined by a graphical depiction of the forward prediction error in exchange rate terms. The five year forward premium is approximated by a sum of five consequent one year forward premiums. FINDINGS

On one month interval, the unbiased forward hypothesis is rejected in the emerging economies. Extending the time horizon to one year, the regression model produces increasingly biased estimates of future exchange rate. The graphical depiction of forward forecast error confirms the findings from the regression model. When comparing the one year bias to five year bias, measured in exchange rate terms, the bias is found to increase along with the extended time horizon. In the majority of the sample countries, on the five year maturity the forward prediction error becomes consistently positive implying that the five year forward rate is a systematically upwards biased predictor of future exchange rate. The impact on hedging performance depends on which currency the entity in question is selling and which currency it is buying with the forward contract. Hedging an emerging market currency denominated foreign exchange risk on a five year horizon has either been systematically profitable or unprofitable throughout the sample.

Keywords Uncovered interest rate parity, unbiased forward rate hypothesis, time horizon effect, emerging economies, foreign exchange, hedging, OTC forward contract

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Aalto-yliopisto, PL 11000, 00076 AALTO www.aalto.fi Maisterintutkinnon tutkielman tiivistelmä

Tekijä Veli-Rasmus Varetsalo

Työn nimi Harhaton termiinikurssi ja aikahorisontti kehittyvissä talouksissa ja vaikutukset valuuttariskien hallintaan

Tutkinto Kauppatieteiden maisteri Koulutusohjelma Rahoitus

Työn ohjaaja Professori Markku Kaustia

Hyväksymisvuosi 2014 Sivumäärä 75 Kieli Englanti

Tiivistelmä

TUTKIELMAN TAVOITTEET

Tutkielman tavoitteena on tutkia harhattoman termiinikurssin hypoteesia kehittyvien talouksien valuutoissa ja aikahorisontin vaikutusta. Tarkoituksena on siis mitata ennustaako valuuttatermiinikurssi harhaisesti vai harhattomasti tulevaisuudessa toteutuvaa valuuttakurssia. Lisäksi tutkielman tavoitteena on analysoida, mikä on tulosten vaikutus valuuttariskien hallintaan kehittyvien talouksien valuutoissa.

AINEISTO JA MENETELMÄT

Aineisto on muodostettu kuukausittaisista havainnoista valuuttakursseja ja termiinipisteitä 1-, 3-, 6- ja 12-kuukauden maturiteeteille. Aineistossa on kymmenen kehittyvää valtiota: Brasilia, Chile, Indonesia, Intia, Etelä-Afrikka, Etelä-Korea, Mexico, Tšekin tasavalta, Turkki ja Venäjä. Valuutta-aineisto on ladattu Bloombergin tietokannasta ja Valuutta-aineiston kaikki valuuttakurssit sekä termiinipisteet ovat noteerattuja Yhdysvaltain dollaria vastaan. Harhattoman termiinikurssin hypoteesia testataan ensin lyhyellä aikavälillä käyttäen Fama-regressiomallia, jossa hyödynnetään Newey-West keskivirhettä. Pidemmän aikahorisontin vaikutusta kokeillaan yhden ja viiden vuoden ajanjaksoilla esittämällä graafisesti valuuttakurssimääräinen ennustevirhe. Viiden vuoden termiini on synteettinen tai keinotekoinen tarkoittaen sitä, että se on estimoitu laskemalla yhteen viisi peräkkäistä yhden vuoden termiinipreemiota.

TULOKSET

Yhden kuukauden aikavälillä harhattoman termiinikurssin hypoteesi hylätään. Aikahorisontin kasvattaminen vuoden mittaiseksi aiheuttaa hypoteesin merkittävämmän hylkäämisen, koska regressiomallin mittaama harhaisuus kasvaa systemaattisesti ajanjakson kasvattamisen johdosta. Graafinen ennustevirheen tarkastelu yhden ja viiden vuoden välillä vahvistaa regressiomallissa todennetun dynamiikan: aikahorisontin kasvaessa termiinin harhaisuus kasvaa. Merkittävää viiden vuoden ennustevirheessä on se, että se on systemaattisesti positiivinen suurimmassa osassa aineiston valuutoista. Positiivinen ennustevirhe tarkoittaa, että viiden vuoden termiini ennustaa tulevaa valuuttakurssia systemaattisesti harhaisesti yläkanttiin eli ennuste on suurempi kuin toteuma. Vaikutus valuuttariskien suojaamiseen riippuu siitä, kumpaa valuuttaa (kehittyvän valtion valuuttaa vai dollaria) entiteetti ostaa ja kumpaa se myy termiinisopimuksella. Valuuttariskin suojaaminen viiden vuoden aikahorisontilla on ollut siten joko järjestelmällisesti tuottoisaa tai tappiollista.

Avainsanat Kattamaton korkopariteetti, harhaton termiinikurssi, aikahorisontti efekti, kehittyvät taloudet, valuuttakurssit, suojaaminen, valuuttatermiini, OTC johdannaismarkkinat

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Table of contents

1 Introduction ... 1

1.1 Introduction to the topic ... 1

1.2 The research question and contribution... 5

1.3 Limitations of research ... 7

1.4 Empirical findings ... 7

1.5 Structure ... 9

2 Literature review ... 10

2.1 Introduction to the uncovered interest rate parity ... 10

2.2 The UIP and the time horizon effect ... 11

2.3 Theories intending to explain the forward premium anomaly ... 13

2.4 Econometric properties and issues of the UIP... 15

2.5 Forward rate unbiasedness in emerging economies ... 17

3 Hypotheses ... 20

4 Data and methodology ... 25

4.1 Data ... 25

4.1.1 Sample data set description ... 25

4.1.2 Variable construction and summary details ... 30

4.2 Methodology ... 35

4.2.1 Newey-West regression specification ... 35

4.2.2 Data overlap discussed ... 35

4.2.3 Monthly rolling regression estimation ... 36

4.2.4 Forward prediction error for one and five year maturities ... 37

4.2.5 The construction of the five year forward rates ... 38

4.2.6 The forward forecast error and the impact on returns from hedging ... 40

5 Results ... 44

5.1 Newey-West regression ... 44

5.2 Time-varying beta estimate: rolling regressions ... 48

5.3 Unbiased forward rate hypothesis for one and five year horizons ... 51

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5.3.2 Long horizon UIP for Chile, Indonesia, Russia and South Africa ... 56

5.3.3 Long horizon UIP for India, Mexico and South Korea... 59

5.3.4 Discussion of distant horizon forward biasedness ... 62

5.4 Hedging implications of the findings ... 65

6 Conclusions ... 68

List of references ... 76

Appendix A: Sample exchange rates ... 79

Appendix B: Five year forward rates: justification behind the construction ... 81

Appendix C: Forward forecast error (bias) for three years maturity ... 82

Appendix D: UIP variables depicted for one and five year intervals ... 84

Appendix E: Forward yields: 1-month against 12-months ... 87

Appendix F: Interview with Metso Corporation foreign exchange risk manager ... 89

Appendix G: Newey-West regression alphas and fitted values plotted ... 91

List of figures Figure 1: Illustrating the research topic: USD/BRL rate and hypothetical forward rates ... 3

Figure 2: Basis for hypothesis 4: USD/BRL rate and hypothetical forward rates ... 23

Figure 3: Variable volatilities illustrated graphically ... 32

Figure 4: Rolling beta coefficient on a monthly interval for a five year window ... 49

Figure 5: UIP one and five year comparison for Brazil, Czech Republic and Turkey ... 53

Figure 6: UIP one and five year comparison for Chile, Indonesia, Russia and South Africa ... 56

Figure 7: UIP one and five year comparison for India, Mexico and South Korea ... 59

List of tables Table 1: FX market imperfections in sample countries and data set description ... 27

Table 2: Currency liquidities (average daily volume in billion USD, 1998-2013)... 29

Table 3: Regression variable mean values and standard deviations ... 31

Table 4: DF-GLS test for unit root... 33

Table 5: The construction of five year forward rates ... 39

Table 6: The forward return and prediction error ... 41

Table 7: The connection between profitability, prediction error and hypotheses ... 43

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Introduction

1.1 Introduction to the topic

“Locking in an exchange rate through a forward contract – the most common way to hedge currency risk – is rarely economic with high-yielding EM currencies”

- The Financial Times1

Multinational companies (MNCs) operate increasingly in the emerging economies, striving to get their share of the rapid growth and profit potential. Only from 2006 to 2013 the foreign direct investment into emerging economies has increased from USD 400 billion to USD 780 billion2. There

are many risks in entering the developing economies and one of them is the foreign exchange (FX) risk, which is completely different from what multinational companies are used to in their standard risk management practices. The predominant approach of MNCs to managing foreign exchange risk is the Over-The-Counter (OTC) foreign exchange market where different instruments, such as forward contracts and options, are available for hedging and other purposes. The OTC FX volume of non-financial customers, which includes MCNs and governments, has increased from a daily average of USD 265 billion in 1998 to a daily average of USD 465 billion in 20133. Despite the OTC market becoming the prevailing avenue of foreign exchange trade for both non-financial and financial counterparties, the emerging market currencies (EM currencies) are still in their infancy in terms of e.g. market liquidity, institutional interventions as well as exchange rate (spot rate) and capital controls4. In addition to the market imperfections that may distort the prices in the foreign exchange market, the emerging market currencies are frequently associated with certain mathematical abnormalities.

Technically speaking one of the foremost challenges with managing, i.e. hedging, a risk in these currencies is that the OTC forward premiums for the emerging market currencies are extraordinarily large. The forward premium, which equals the difference between an exchange rate now and a forward rate agreed to a future date, has a very intuitive explanation: It is approximately equal to the

1 FT.com. Darren Smith, HSBC head of corporate FX sales. The Financial Times, May 26, 2014. 2 World investment report 2014, by United Nations.

3 Triennial central bank survey of foreign exchange and derivatives market activity in 2013. Issued by Bank for

International Settlements (BIS).

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difference between the interest rates in two countries for the specified maturity. The problem is that for countries classified as emerging, or developing, the interest rates are high in comparison with advanced or developed economies; e.g. in 2010 the average US dollar 12-month deposit rate was 0.9% whereas the average 12-month risk-free Brazilian real rate was approximately 9.5%5. For Brazilian real, this a historically low rate; in 2003 it was on average 16%. This discrepancy is called the interest rate differential and it equals the forward premium. When the maturity of the forward is extended from the specified one year, the premium may grow to an even more significant scale.

Another technical challenge in hedging with emerging market currencies is that the exchange rates are presumed to have been on a continuously declining trend. If the exchange rate is experiencing an ongoing decline, the forward rate agreed to now will be larger than the exchange rate that materializes in the future, unless, the forward premium is negative. As illustrated, the forward premium in the case of Brazilian real is nowhere near negative, on the contrary, it is positive and substantial. With these two combined, a foreign exchange risk manager is puzzled. If a forward contract is entered under a trend of exchange rate decline and the forward premium is substantial, the forward rate will be considerably higher than the exchange rate that materializes in the future. The practical implication is that the difference between a forward rate and a future exchange rate is the definition of profit or cost of a forward contract or hedge. Furthermore, when the maturity is extended to multiple years, logically, the forward premium escalates even further. This leads to the question that exactly how biased predictor of future exchange rate the forward rate is?

Figure 1 illustrates the discussed presumed challenges in hedging a foreign exchange risk in emerging market currencies using OTC forward contracts. In the figure, the historical US dollar against Brazilian real exchange rate is depicted and, in addition, hypothetical forward rates for different maturities, namely from one to five years. Especially for the first set of forward rates, when the maturity is extended from one to five years, the discrepancy between the forward rate and the future exchange rate increases substantially (see the vertical dashed lines). Depending on the size of the forward premium for different maturities and the extent of the exchange rate decline, the forward rate may be highly upwards biased predictor of future exchange rate, especially at a time horizon of multiple years. If such dynamics were to be found, the implication would be consistent profitability or costliness depending upon the entity in question.

5 Computed from the data set. The 2010 interest rate differential is not abnormally considerable even though the US dollar

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Figure 1: Illustrating the research topic: USD/BRL rate and hypothetical forward rates

Figure 1 shows the actual historical USD/BRL (US dollar, Brazilian real) exchange rate during 1999-2014. In addition there are two theoretical forward rate lines starting in 2005 and 2008 respectively. They illustrate the difference between committing to one, two… or five year forward rate: marked as (𝑓𝑡1,2…5), where the superscript denotes the maturity in

years. The dashed lines are the differences to current spot exchange market, i.e. the forward rate prediction error or yield. The point is to show that the substantial forward premiums in conjunction with the trend of appreciating emerging market currency may result in highly costly commitments.

The controversy concerning the relationship between the forward rate and the future exchange rate is not entirely a novel idea as such. As a matter of fact, it is perhaps the most studied theory in the field of international finance, known as the uncovered interest rate parity (UIP) or the unbiased forward rate hypothesis6 (for a review see e.g. Engel, 1996; Froot and Thaler, 1990). The reasons for its popularity as a research topic are its importance for the participants in the foreign exchange market, theory’s intuitively appealing relationship and, lastly, the invariable finding that the uncovered interest rate parity fails. The OTC FX market is simply massive; in 2013 it reached a daily volume of 5.3 trillion US dollar7, out of which the proportion of currency forwards and swap derivatives is substantial. Given the market is highly liquid, intuitively the forward rates could be assumed to have

6 Unbiased forward rate hypothesis is analogous to uncovered interest rate parity if the covered interest rate parity is

assumed to hold (Engel, 1996). The literature convention is to use these terms interchangeably which is done in this thesis as well.

7 Reuters.com. Published Sep 5, 2013.

𝑓𝑡1 𝑓𝑡2 𝑓𝑡3 𝑓𝑡2 𝑓𝑡3 𝑓𝑡5 𝑓𝑡4 𝑓𝑡4 𝑓𝑡5

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some meaningful relationship to the future exchange rates. However, regardless of countless of attempts, there have been surprisingly few studies finding that a forward rate would be to any degree predictive of future exchange rate (Engel, 1996; Rossi, 2013). Moreover, the abundant articles have not even reached a consensus as to why the uncovered interest rate parity systematically fails, hence the term forward premium anomaly (Engel, 1996).

A promising branch of literature has examined the impact of extending the time horizon from the traditional one month to even decades. Lothian and Wu (2011) and Snaith, Coakley and Kellard (2013) find that in the advanced economies, the uncovered interest rate parity holds well at distant horizons i.e. that the forward rate becomes an unbiased or accurate predictor of future exchange rate. Snaith, Coakley and Kellard (2013) argue that the UIP holds already at a three year interval and, furthermore, they find a continuous tendency of the forward rates to become more and more unbiased as the time horizon is extended step by step. Given that in addition Chinn (2006) finds concurring evidence, it can be concluded that the current consensus is that the UIP holds better for longer time periods in the advanced economies.

Emerging market currencies introduce a new, curious, twist to the uncovered interest rate parity. First of all, the interest rate differentials are as if from a different planet. As mentioned, the difference between the risk-free interest rates of US dollar and Brazilian real was at 9%, under a low interest rate environment. Under similar circumstances, the interest rate differential between the US dollar and euro was approximately 0.35%8. Moreover, according to Lothian and Wu’s (2011) data set description, the interest rate differential has been relatively low between advanced economies also historically. Secondly, the emerging market currencies are mostly less liquid than the major currencies and the foreign exchange markets are frequently imperfect (Doukas and Zhang, 2013). The final characteristic making the emerging markets a unique test environment is the well-known investment strategy called carry trade. The renowned profitability of carry trade is indicative of a violation of the uncovered interest parity but it is not a direct test of the UIP as such (Menkhoff, Sarno, Schmeling and Schrimpf, 2012). Nevertheless, one could expect the forward premium anomaly to be exceptionally severe in the emerging economies given the shown profitability of carry trade. The studies of the parity theory in emerging economies are extremely scarce. In one of the few existing studies Frankel and Poonwala (2010) find, to all surprise, that the interest rate differentials are less biased predictors of future exchange rates in emerging economies in comparison to advanced

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economies. Therefore Frankel and Poonwala (2010) propose that the parity holds better in emerging economies.

1.2 The research question and contribution

This study examines the unbiased forward rate hypothesis and time horizon effect in emerging economies using OTC forward rates. The UIP and its relationship to time horizon has been examined in advanced economies by e.g. Snaith, Coakley and Kellard (2013) and Lothian and Wu (2011), but for emerging market currencies the time horizon effect has not been studied to best of my knowledge. However, with the regular short, one month, interval, the UIP has been already tested in the emerging economies by Frankel and Poonwala (2010). My study differs from the paper by Frankel and Poonwala (2010) not only by investigating both short and long maturities but in addition by having six years of more data. Moreover, this study differentiates from all of the aforementioned by using the actual OTC forward quotes instead of interest rates. In addition, this study intends to address more accurately the nature of the UIP failure: Will the forward rate become increasingly one-sidedly biased given the emerging market presumed tendencies as illustrated in figure 1?

I examine the unbiased forward rate hypothesis in two distinct phases. First, for short maturity data of 1-, 3-, 6- and 12-months, the literature standard test Fama regression is run. The Fama regression consist of two logarithmic variables, the change in exchange rate and the forward premium. Thus, the regression intends to explain the variation in exchange rate with the variation in forward premium. The regression is run for all maturities using monthly data which creates a data overlap problem. To address this issue, Newey-West standard errors are employed. However, according to Snaith, Coakley and Kellard (2013), the Newey-West standard errors are only a part of the answer to the data overlap issue. Because the overlap is expected to become excessively pronounced, for the maturities above 12-months the unbiased forward rate hypothesis is tested with an alternative method. Another reason for the change of methodology is that both in the previous academic literature and in this paper it is found that the Fama regression model has serious downfalls. The forward premium is known to exhibit a highly steady behaviour whereas the exchange rate is extremely volatile. In addition, potential time series breaks affect the regression specification.

In the second phase of the research, the unbiased forward rate hypothesis is tested for one and five year horizons by graphically plotting the forward rate bias or prediction error that is measured in exchange rate terms. The forward rate prediction error equals the difference between the forward rate and the exchange rate that the forward rate intended to predict (the dashed line in figure 1). It is

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deduced from the Fama regression variables and hence it is a comparable test of unbiased forward rate hypothesis. The strength of this approach is that the prediction error is a more accurate measure of forward rate biasedness than the regression beta estimate. Also the statistical issues related to the Fama regression including a low coefficient of determination and differences in variables variances may be neglected. Furthermore, the forward prediction error is a direct measure of forward contract yield applied by industry professionals. Hence the impact of biasedness on profitability is directly computable from the findings. In addition to the implications to profitability, the graphical depictions of one and five year biases are discussed and compared to each currency’s market imperfections, foreign exchange volume, historical exchange rate development and average size of forward premium.

The five year forward rates used in this study are not actual OTC five year forward rates given the lack of data available. Instead they are synthetic in nature implying that the five year premium is approximated using the one year premiums. The five year premium is computed by adding up five consequent one year premiums, creating a seamless five year time line similarly as the actual five year premium would do. For illustration, the five year rates in figure 1 can be perceived as being constructed from subsequent one year premiums and the initial exchange rate. Alternatively, the five year forward premium could have been approximated by multiplying any given one year premium by five and the findings would not have been altered substantially because the forward premium has been so static during the sample. According to the foreign exchange risk manager of Metso Corporation, Mikko Vainikka, the selected method of computing cumulative one year premiums serves as a prudent proxy for the actual five year premium because the actual OTC traded five year premiums often carry an additional premium given the regulations on the OTC derivatives.

The sample data consists of end-of-month mid-quotes for exchange rates and forward points, extracted from the Bloomberg terminal. Time period is from the beginning of 1999 until the start of year 2014, a selection stipulated by data availability. The forward points retrieved from Bloomberg terminal range from 1-month to 12-months. The countries chosen are Chile, Brazil and Mexico (South- and Central America), Czech Republic, South Africa and Turkey (EMEA9) , India, Indonesia and South Korea (Asia) and Russia. Criteria included geographical diversification, foreign exchange market functionality and, especially, data availability.

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1.3 Limitations of research

The primary limitations of this research are the data availability, data overlap, incomplete time series robustness tests and the somewhat assumption based analysis of long-term results. The emerging market currency data is only available from 1999 onwards which is distinctively less than for major currencies, having valid data since 197310. The small sample size introduces peso problems, referring to low probability and high impact events that do not have time to materialize in small samples. Hence, it is pivotal to utilize all information available, leading to the selection of monthly data. Regressing variables with longer than one month horizons on a monthly data creates a data overlap issue, resulting in a moving average error process. This is relieved using Newey-West robust standard errors, a technique exercised in similar studies (e.g. Snaith, Coakley and Kellard, 2013; Beber, Breedon and Buraschi, 2010). In addition to the data overlap, the time series properties of the forward premium are slightly problematic. A thorough analysis would require the application of a mean-break detection methodology given the forward premium has been shown to have structural breaks (Baille and Cho, 2014). Another challenge is that the distant time horizon examinations of the forward prediction errors are analysed against slightly presumed market frictions because explicit data on e.g. the size and frequency of institutional interventions in emerging economies are rarely available. Finally, the five year forward rates are synthetic instead of actual rates.

1.4 Empirical findings

I find that the unbiased forward rate hypothesis in emerging economies is rejected in the short-term and, moreover, that the bias increases systematically with extending the time horizon, regardless of whether it is measured with the regression or the prediction error. Firstly, the proposition of Frankel and Poonwala (2010) of lesser biased short-term forward rates in the emerging economies is rejected according to the interpretation of the Fama regression findings. Secondly, the time horizon effect is found to be reversal to advanced economies; the forward bias escalates the further the maturity is extended. Finally, when the time horizon is extended sufficiently, i.e. from one to five years, the forward rate bias becomes positive consistently throughout the sample, implying that the five year forward rate is a systematically upwards biased predictor of future exchange rate during the sample time series. Especially the last-mentioned has drastic implications to hedging profitability.

The Fama regression result interpretation is carried out by considering only the statistically significant slope coefficients. The unbiased forward rate hypothesis is rejected at the one month interval given

10 However, the OTC forward data even for major currencies may not be this lengthy. Those studies frequently use interest

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the majority of the beta coefficient estimates are negative. The only outlier is Russian ruble, which has a beta close to unity but the exchange rate against the US dollar is highly controlled. When the maturity is lengthened incrementally to 12-months, for the currencies that the beta attains statistical significance, the bias increases systematically. In the regression, the forward bias is defined as the distance of the beta estimate from the desired unity value. In the advanced economies, the relationship has been found to be the opposite; increasing maturity inclines betas towards unity (Snaith, Coakley and Kellard, 2013). This is the main contribution: Increasing the maturity in the emerging market forward rates produces systematically more biased estimates of future exchange rate.

The increase of forward bias together with maturity is confirmed with the graphical depiction of the forward prediction error for one and five year maturities, which is measured in exchange rate terms. The prediction error of five year forward rate is consistently greater than the prediction error of the one year forward rate for the majority of countries (Brazil, Chile, Czech Republic, Indonesia, Russia, South Africa and Turkey). Furthermore, the five year bias in these markets is continuously positive nearly throughout the sample. Positive prediction error signifies that the five year forward rate is an upwards biased predictor of future exchange rate. This is exactly what is assumed in the figure 1 and the preceding discussion. The extension of maturity results in the emergence of a systematic upwards forward bias. But is the reason in the size of the forward premium or in the trend of exchange rate decline?

As the figure 1 demonstrates, there are only two mathematically plausible explanations for a consistently upwards biased forward rate; either the exchange rate has been on a declining trend all through the sample and/or the forward premium is sufficient to make a difference. These two factors vary in their significance between the currencies. For the Chilean peso and Czech koruna, the determinant of positive prediction error is mainly the trend of declining exchange rate given the average forward premiums near zero and the forward prediction error closely mimics the exchange rate developments. However, Brazilian real, Indonesian rupiah, Russian ruble, South African rand and Turkish lira experience at least some degree of exchange rate increase which means the forward premium has been sufficiently large to maintain the positive prediction error. Concurringly, for these currencies the average forward premiums are the sample highest. The most radical forward premium is in Turkey, and, interestingly enough, the Turkish lira against US dollar exchange rate has been on a remarkable surge during the sample (from USD/TRY 0.5 to USD/TRY 2.0). Nonetheless, the forward rate bias is consistently positive. The other exchange rates also experienced relatively substantial appreciation especially in the aftermath of the financial crisis in 2008 but the five year

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rates remain upwards biased. Thus for these countries, it is the excessive size of the forward premium that accounts for the existence of a consistent positive five year bias. Neither the diverging market imperfections nor the foreign exchange volumes appear to convincingly explain the differences in the behavior of the forward bias in different currencies.

A practical implication of a systematic positive five year forward bias is that committing to a five year forward rate has been either systematically profitable of loss-making depending on which currency the entity is selling and which buying with the forward contract. The forward has been unprofitable if the forward is agreed to sell emerging market currency and buy advanced market currency (US dollar) and profitable if the forward has been agreed to buy emerging market currency and sell USD. The profitable alternative is analogous to the profitability of carry trade because the effective impact of such forward rate is to take a speculative view, or long position, in the emerging market currency. The implication to hedging is that carrying out risk management that involves committing to the described unprofitable forward rates has been resulting in loss through the entire sample. For instance, these forwards could be used to hedge sales of an advanced economy based company that are denominated in emerging market currency. According to Metso Corporation, many industrial companies currently have well predictable distant horizon inflow from emerging economies given the increased popularity of long-term industrial service contracts. The strength of aforementioned findings does not stem from a statistical method e.g. computing an average profit or using a mean-variance optimization. Instead, it is based on the finding of a systematic and consistent positive bias, throughout the sample.

1.5 Structure

First, I will discuss the surrounding literature from forward rate unbiasedness tests to suggested explanations of the forward premium anomaly, which is followed by the presentation of the hypotheses set for this research. Then the data set is described and analysed, followed by the presentation of the methodology, including the Fama regression model and the derivative return specification. Finally, results are presented and discussed in conjunction with the findings from the existing literature. The conclusions section completes this paper.

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Literature review

In this section I review the literature most relevant for this research. First, the uncovered interest rate parity is introduced on a general level followed by discussion of most prominent empirical results. The standard tests of the uncovered interest parity are run with a monthly data interval employing a regular regression model. Second, the impact of extending time horizon as well as the impact of employing alternate versions of the regression model are discussed. All in all, these empirical findings are mostly in agreement with each other; in short, the parity theory is rejected. Therefore, the third part of the literature review presents the main explanations of the parity failure, including central bank interventions, time-varying risk premium and econometric misspecification. The final part of this chapter introduces the few studies that deploy emerging market currency data.

2.1 Introduction to the uncovered interest rate parity

The uncovered interest rate parity belongs to the branch of international finance literature that intends to forecast exchange rates, see e.g. Rossi (2013) for a great review. Other factors often used to predict FX rates include price and inflation differentials as well as output and productivity differentials. The UIP is, however, fundamentally different from these other predictors because the interest rate differentials it examines are the basis of FX forward rates. Moreover, the OTC foreign exchange market is incredibly liquid; in 2013 it reached an average daily volume of over five trillion US dollars11, implying that the forward rates are of significant practical importance. In addition to the interested counterparties in the foreign exchange market, the academic intrigue for studying the uncovered interest rate parity is considerable stemming from the research findings. In summary, the uncovered interest rate parity, or the unbiased forward rate hypothesis, has been consistently rejected and, moreover, the academic literature has found it difficult to explain why (Engel, 1996).

The theory behind the UIP is relatively simple: two currencies have two different interest rates and for the investments to be equally attractive, the exchange rate should be expected to appreciate or depreciate in accordance with the difference in these rates. For example suppose the one year dollar interest rate is 10% and the comparable euro interest rate is 6%, then the interest rate differential is roughly 4%12. Thus risk neutral and rational investors should expect the dollar to depreciate by 4%

against euro over the next year (Froot and Thaler, 1990). This relationship is called the uncovered interest rate parity. From the above dynamics it results that the interest rate differential equals the

11 http://www.reuters.com/article/2013/09/05/bis-survey-volumes-idUSL6N0GZ34R20130905

12 This is not exactly correct but the presentation in corresponding literature is always similar. The correct definition is

that the dollar would be excepted to depreciate by = 1 – [(1+10%)/(1+6%)] = 3.7% which is only approximately equal to the simplified calculation above.

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forward premium of a forward rate that has the same maturity as the interest rates. Otherwise there would be a direct arbitrage opportunity, assuming all these instruments are accessible, a theory known as the covered interest rate parity (Engel, 1996). The foundation of the forward premium is particularly interesting since it is a pure mathematical computation and not, at least directly, reflecting the market expectations of future exchange rates.

2.2 The UIP and the time horizon effect

The forward rate unbiasedness is frequently examined with the following, previously cited as, Fama (1984) regression: (𝑠𝑡+𝑖− 𝑠𝑡= 𝛼 + 𝛽 (𝑓𝑡𝑖 − 𝑠𝑡) + 𝜀𝑡+𝑖), where (𝑠𝑡+𝑖− 𝑠𝑡) is the change in exchange rate and (𝑓𝑡𝑖 − 𝑠𝑡) is the forward premium, i.e. the difference between spot rate now and the forward rate for time period i. In the Fama regression model the null hypothesis tested is (𝛽 = 1) and (𝑎 = 0) under the assumptions of risk neutrality and rational expectations (Froot and Thaler, 1990). Froot and Thaler (1990) survey evidence from previous studies concluding an average (𝛽 = -0.88) over 75 studies which implies a clear rejection of the null hypothesis. In a more recent study using short horizon data and traditional methods, Frankel and Poonawala (2010) find an average (𝛽 =

−4) for developed economies with a sample of 1996 – 2004. In a survey covering mainstream currencies, Engel (1996) points out a corresponding average beta estimate over an abundance of articles. It can be concluded that slope estimates in range of (−0.5 ≤ 𝛽 ≤ −4) are all consensus values for advanced economies when short horizon data is used. Thus, it is difficult to establish a precise benchmark for a beta estimate for this study.

When the time horizon is extended from the traditional one month, there is a slight consensus of better performance of the uncovered interest rate parity for the established market currencies. Snaith, Coakley and Kellard (2013) suggest that the unbiasedness emerges between two to five year horizons depending on the exchange rate in question. They run the Fama regressions with monthly observations from a sample consisting of historically the most liquid currencies: Canadian dollar, Deutsche mark, Japanese yen, Swiss franc and the US dollar. Lothian and Wu (2011) provide supportive evidence of the time horizon effect as they find unbiased slope estimates using currencies French franc and the US dollar against the British pound with a sample ranging from 1803 to 1999, for both short- and long-term variables with the latter with greater predictive ability. However, on a critical note, out of these two exchange rates only one, franc against sterling attains a beta statistically not different from one, while the other does not. The USD/GBP actually remains quite far from the desired unity value with betas of 0.14 (short rate) and 0.38 (long rate). Hence, based on one currency pair out of the two possible Lothian and Wu (2011) make a conclusion that the uncovered interest

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rate parity holds when the period is extended sufficiently. In addition, they find that the beta estimates do become negative, concurring with the existing literature, when the sample is dominated by observations from the recent decades.

There is also evidence proposing that the uncovered interest parity does not improve with longer horizon but instead is dependent on the exchange rate. Bekaert, Wei and Yuhang (2007) find using a vector autoregression (VAR) that the parity holds well for certain currencies regardless of the time horizon, namely the US dollar against Deutsche mark, but reject the hypothesis for all maturities for GBP/USD and GBP/DEM. The sample construction is quite similar to other studies as it consists of established currencies, monthly observations and data from 1971 to 1996. Thus, at this point, the results can be interpreted quite valid evidence against any time period conditional dynamics in the parity relationship. However, again a more exact scrutiny reveals that with one of the two model specifications, Bekaert, Wei and Yuhang (2007) actually do accept the UIP for long horizon only, for the GBP/ USD pair. This leads to question of the impact of the intrinsic model specification and the variable selection to the regression output. Furthermore, Snaith, Coakley and Kellard (2013) argue that vector autoregression is not a well suited method for testing the horizon effect because, if misspecified, the interpretation of long-run results in particular becomes unclear. Nevertheless, the horizon effect did not pass the VAR inspection even with a fairly large sample.

The uncovered interest rate parity has also shown to depend on the time period of the sample given that different studies have found similar beta coefficient estimates for similar time periods. These examinations have been mainly conducted with rolling regressions with an appropriate window. With their sizable data set covering two centuries, Lothian and Wu (2011) run rolling regressions finding that the beta estimates became negative only when the subsample is dominated by the 1970s or the 1980s. In agreement, using a five year window in regressions, Baillie and Bollerslev (2000) find that slope coefficient is highly variable and that it is especially negative during the 1980s. Also Baillie and Cho (2014) verify these observations and in addition note that the 1990s experience substantial negative beta estimates that are occasionally followed by a reversal effect after the year 2008. These findings suggest significant time variation in the parity relationship. In particular, the discovery of changing dynamics after the middle 1970s concurs with the date of termination of the fixed exchange rate regime. Hence, extending the sample beyond the floating rate era which generally started in 197313 should be questioned and the conclusions drawn from such studies be properly challenged.

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2.3 Theories intending to explain the forward premium anomaly

Although, explaining the existence of the forward premium anomaly is not in the primary objectives of this research, it is beneficial to go through the most important articles covering this area since it allows a more thorough discussion of the results to be discovered. The proposed explanations are abundant, including a time-varying risk premium, investor estimation errors, peso problems, omitted impact of central bank interventions and econometric misspecification. None of these theories have been generally accepted as a consensus explanation for the historical failure of the uncovered interest rate parity.

One of the most popular explanations in the academic literature has been the risk premium approach, which proposes that conditional on efficient and rational forward market, any forward rate can be broken down into expected spot rate 𝐸(𝑠𝑡+𝑖) that is a rational and efficient forecast given all

information available and a risk premium (Fama, 1984). Thus, in equation form the forward premium can be broken down as follows, where the first term in brackets is viewed as the risk premium: 𝑓𝑡𝑖 −

𝑠𝑡 = [𝑓𝑡𝑖 − 𝐸(𝑠

𝑡+𝑖)] + [𝐸(𝑠𝑡+𝑖) − 𝑠𝑡] (Backus, Foresi and Telmer, 2001). This definition stipulates

the following statistical requirements for the risk premium: given the found negative beta coefficient estimate, variance in the risk premium should exceed the variance of expected spot return (𝐸(𝑠𝑡+𝑖) −

𝑠𝑡). This property has been proven particularly difficult to document (Maynard and Phillips, 2001).

The academic literature has repeatedly failed in endeavours to reconcile the Fama (1984) requirements for a risk premium and empirical findings (Engel, 1996).

The Fama’s (1984) definition of a risk premium is still of academic intrigue as it has been attempted to include in novel methods of explaining the failure of uncovered interest rate parity. Backus, Foresi and Telmer (2001) test affine term structure models, which have been found to estimate well single-currency yields, by restricting the pricing kernels by the statistical conditions of the Fama’s time-varying risk premium. They conclude that the affine models do not explain or have difficulty in explaining the forward premium anomaly. In addition, there have been several models that have intended to statistically model the risk premium, even general equilibrium models that consider consumer utility functions for domestic and foreign output as well as portfolio-balance models that optimize utility from domestic and foreign fixed income investments (Engel, 1996). However, with any plausible degree of risk aversion and standard models, the risk premium has been proven difficult to validate (Engel, 1996).

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A logical extension of the risk premium approach has been to investigate whether foreign exchange volatility accounts for the forward premium anomaly. The studies modelling volatility have been somewhat successful, if a positive, yet different from unity, estimate can be perceived as such. Clarida, Davis and Pedersen (2009) run the one month Fama regression and find negative slope estimates only for low volatility states and positive, yet different from unity, estimates for high volatility states. Volatility is defined as the standard deviation of returns for a 3v3 carry trade portfolio. The 3v3 carry portfolio is constructed by equal weighted long positions in the three highest yielding and short positions in the three lowest yielding currencies. To define the FX volatility through carry trade returns might be slightly problematic because it takes into account only a proportion of currencies in the sample and the yields by construction consider not only the exchange rate market but also the interest rates. Another novel proponents of time-varying risk premium approach are Beber, Breedon and Buraschi (2010) who study the impact of heterogeneous beliefs on foreign exchange implied volatility and future currency returns. They find that the effect of increased funding liquidity problems14 turns short-term Fama regression slope estimate from negative to positive while controlled with a difference in beliefs variable15. Given that the dispersion in beliefs attained statistical significance, it was concluded to be a risk factor in the currency markets, and thus supportive of the time-varying risk premium explanation of the forward premium anomaly.

The institutional interventions and other market imperfections are another innovative point of view. Mark and Moh (2007) examine the impact of central bank interventions on the uncovered interest rate parity. They find run the Fama regression separately for so called institutional intervention periods and non-intervention periods for USD/DM and USD/JPY with a weekly data16. They find betas closing the unbiased forward rate hypothesis when the interventions are excluded, proposing that the interventions account for the anomaly. The obvious problem with the study is that it employs a one week time interval which is unconventional and thus infeasible for a direct comparison. Also the amount observations in the intervention periods is extremely low. Nevertheless, the potential for an institutional intervention to substantially impact the uncovered interest rate parity condition is an interesting approach, because it seems only rational that if the central bank either intervenes directly the markets using its reserves, the exchange market is immediately distorted, or the central bank

14 Funding liquidity is measured with TED spread: The difference between three-month London Interbank Offered Rate

(LIBOR) Eurodollar rate and the three-month US T-bill rate.

15 Measured with analyst forecasts of exchange rates in Reuters. 16 US dollar against Japanese yen and US dollar against Deutsche mark.

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adjusts its key interest rates directly altering the interest rate differential17. All these economic explanations appear feasible but none of them achieves a truly dominant status, resistant of acute critique. From such disparate findings emerge the controversy for the econometric foundation of the variables employed in the regressions.

2.4 Econometric properties and issues of the UIP

The empirical studies recurrently encounter similar issues in their examinations: The models have low R-squared ratios, the exchange rate has substantially greater variance than the forward premium and the forward premium displays persistent autocorrelations. Especially the extremely low variance of the forward premium is of paramount concern. In addition, small sample size is often found problematic.

One of the foremost obstacles confronted in all studies of unbiasedness or UIP is the nearly always recorded low R-squared ratio or the coefficient of determination. The R-squared measures the proportion of variance of the dependent variable that is explained with the variance of the independent variable. This ratio has often been in the scale of 1% - 5 % which means that the forward premium explains only a few percentages of the changes in the exchange rate in question (see, e.g. Backus, Foresi and Telmer, 2001; Frankel and Poonwala, 2010). Furthermore, it is indicative of low goodness of fit of the models deployed. Taking all this under consideration, it would be easy to conclude that the model specification should be improved by including omitted variables or by fitting a more advanced statistical method than the standard OLS regression. However, it needs to be emphasized that despite abundant effort there is neither single specific model that would have been proven a superior fit nor any consistent success achieved by introducing new variables (Rossi, 2013).

The notably lower variance of the forward premium has orientated a branch of the literature towards scrutinizing its impact on the time series properties of the variables. The exchange rate is often documented to have unit root and to be stationary at first difference which implies that the variable deployed, (𝑠𝑡+𝑖− 𝑠𝑡), is stationary (Engel, 1996). The complication arises from the unclear nature of the forward premium and the implications of explaining changes in a stationary spot series. If the forward premium is concluded non-stationary, i.e. it has an order of integration of (0.5 < 𝑑 < 1), then estimates of 𝛽 are inconsistent (Maynard and Phillips, 2001). On other hand, if the order of integration is in between (0 < 𝑑 < 0.5), 𝑓𝑡𝑖 − 𝑠𝑡 is stationary and estimates of 𝛽 are consistent and

17 Assuming that risk-free deposit rates are based on central bank reference rates. On the other hand, for long-term rates

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the Fama regression is balanced (Engel, 1996; Maynard and Phillips, 2001). Maynard and Phillips (2001) find that the premium is non-stationary with estimated range: (0.5 < 𝑑 < 1). This result implies a fractionally integrated process where the forward premium has a long-memory and is highly persistent. Hence, Maynard and Phillips (2001) reject the unbiasedness hypothesis in the test’s current construction, suggesting an introduction of some unknown omitted variable to balance the equation. There are, however, difference of opinion in the literature as the forward premium has frequently been found stationary (Engel, 1996). Baillie and Cho (2014) arrive on different implications as they propose that the premium in fact does not have a constant order integration at all but instead it fluctuates through time resulting from structural breaks.

The time series properties of the spot and forward rate are far from consensus and the possibility of omitted variable bias is often expressed but also infinite sample issue has been discussed (Maynard and Phillips, 2001). Baillie and Bollerslev (2000) take a novel approach in considering an artificially generated time series for (𝑓𝑡𝑖) and (𝑠𝑡+𝑖). They suggest that the forward premium anomaly may be viewed as a statistical artefact given small sample sizes and persistent autocorrelation in the forward premium. Sakoulis, Zivot and Choi (2010) proceeds with these finite sample issues by carrying out Monte Carlo simulations of the Fama regressions with and without the inclusion of structural breaks. They find that, on the contrary, when the structural breaks in the mean of forward premium are accounted for, the forward premium is not anymore as persistent as it is perceived to be. In more detail, Sakoulis, Zivot and Choi (2010) show that the unbiasedness should not be rejected based on e.g. the traditional Augmented Dickey-Fuller tests for unit root, because they produce a distorted values as such. They also find that if the breaks are not incorporated the beta estimates are biased downwards, away from the desired unity coefficient.

The issue with the simulated sample sets of, such as Baillie and Bollerslev (2000) as well as Sakoulis, Zivot and Choi (2010), include the lack of economic explanation as well as infeasibility to time horizon effect examination. Even though the forward premium’s structural breaks or the long-memory would to some extent explain the anomaly, the aforementioned studies do not properly account for the economic rationale behind the findings. Why is there a structural break and why exactly does it make the regression estimates biased? As the forward premium has a very low variance, it is difficult to accept that the one time it changes substantially the effect should be excluded from the analysis. Furthermore, I presume the simulation models always have some author sensitive, subjective restrictions on the data formation process that may lead to significantly different results

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between studies. The statistical properties of the sample data set in this study will be extensively discussed in the data and results sections. Especially the low variance of the forward premium and its applicability to a regression model in general are of great interest.

2.5 Forward rate unbiasedness in emerging economies

The emerging market currencies provide a novel spark to the traditional tests of forward rate unbiasedness given the exchange rates function in a fundamentally different manner and given the currencies are often used as the investment currencies in carry trades (see, e.g. FT.com18). The emerging market exchange rates against US dollar are presumed to have been on a declining trend and to have substantial forward premiums. Both of these indicate to an extensive failure of the uncovered interest rate parity but surprisingly, the academic literature currently suggests that the forward rates are less biased in the emerging economies in comparison to advanced economies (Frankel and Poonwala, 2010). Currently the literature examining the unbiased forward rate hypothesis in the emerging economies is extremely scarce.

The carry trade is based on a strategy of investing in high yield currencies, commonly EM currencies, and funding the investment with a low-cost currency, such as Japanese yen or US dollar (see, e.g. Menkhoff, Sarno, Schmeling and Schrimpf, 2012; Clarida, Davis and Pedersen, 2009). The profitability of the strategy is basically based on the failure of the uncovered interest rate parity: The EM currency is not expected not depreciate sufficiently to make the investment unprofitable. However, the carry trade studies are not clear tests of the uncovered interest rate parity because the portfolios are often adjusted monthly to have a basket highest yielding currencies, in which case the currencies invested in may fluctuate during the sample and the exact proportion of investment currencies during the carry are seldom reported (Menkhoff, Sarno, Schmeling and Schrimpf, 2012; Doukas and Zhang, 2013). Nevertheless, the finding of profitable carry trade strategies leads to presume that the forward bias anomaly could be fundamentally different from what has been historically documented for major currencies.

The number of studies measuring the forward rate bias in emerging economies is relatively limited. Mostly this is probably due to the scarce amount of FX data and in some cases quite regulated markets. Both the time horizon and basic monthly data comparisons have been carried out to a slight extent. Frankel and Poonwala (2010) study the short term UIP for a sample of 14 emerging market

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currencies with non-overlapping data for a period of 1996 – 2004. They reject the null hypothesis of (𝛽 = 1) but when comparing to industrialized economies for the same time period, they find an average (𝛽 = −4.3) for the advanced economies, while for emerging economies they find 𝛽 to average slightly over zero with more positive than negative coefficients. They conclude this result being indicative of less bias in the interest rate differential of developing FX markets. This interpretation defies intuition because it is common knowledge that there is less liquidity and more frictions in these markets. Furthermore the widely documented profitability of carry trade strategy suggests that the UIP should fail particularly in these examinations, not the other way around.

The volume of articles examining the term effect in emerging economies is clearly in need of complementing studies. The only studies I found where papers by Kumar and Trück (2014) exploring unbiasedness and risk premiums in the Indian currency futures markets and by Sarmidi and Norlida (2011) examining UIP for different time horizons for 15 emerging markets. Kumar and Trück (2014) run the Fama regression for 1-month through 3-month futures contracts on Indian rupee (INR) against the US dollar (USD). They reject unbiasedness for two and three months with (𝛽 = 1.8) while for the 1-month period the null hypothesis is not rejected. This finding, more in favour of the UIP for short horizons, is conflicting with the evidence from advanced economies as discussed in section 2.1. However, when more currencies are included, the impact of time horizon reverses to correspond with existing literature19. Sarmidi and Norlida (2011) study with interest rate differentials for one, three and twelve month intervals finding positive but rejected coefficient estimates for short horizon while the 12-month period brings 𝛽 estimates close to unity as stated by the UIP. Their data set ranges from 1995-2009, and is composed of deposit rates instead of forward rates and the currency pairs are mixed and matched with three major currencies. These aforementioned studies are clearly in need of supplementing research.

All in all, the literature has found that UIP does not hold well with actual data and the explanations are abundant. For major currencies the betas are found to be significantly different from unity and even having a negative sign, which means that the parity does not even estimate correctly the direction of the change in exchange rate. However for the major currencies, long time horizons have produced some improvement in results. The explanations of the forward premium anomaly include peso problems, heterogeneous beliefs, persistent autocorrelation of the forward premium, finite sample

19 Futures differ from forward contracts since the former are marked-to-market daily and they can only be issued for

specific dates and in specific currency lots. Forwards are, on the contrary, executable for any banking day for any underlying amount and, moreover, for a hedger, their counterpart is a bank while in futures it is an exchange.

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bias, institutional interventions and time-varying risk premium. Out of these, the most promising results have generated the econometric examinations and from economic perspective the effects of central bank interventions. The emerging market currencies provide a new and presumably highly fruitful testing ground for these established theories of uncovered interest rate parity since the EM currencies are novel, still quite frictional in functionality and have far greater variable values and variances to the extent that hedging the foreign exchange exposures has become a predominant source of headache for multinational companies’ risk managers.

The hypotheses are formed in two distinct parts. The first set of hypotheses is more based on the aforementioned literature review; given the finding that the uncovered interest rate parity has been predominantly rejected for the standard one month maturity as well as to perform better along with extended time horizon, the same dynamics are expected to be shown in the emerging economies. The regression model is estimated to produce different from unity beta estimates at the short interval but to approach unity along with extended time horizons. The second part of the tests executed is not equally similar to previous academic papers neither in terms of methodology nor hypotheses. Given the several econometric issues that have been assumed to impair the Fama regression model, I will use a different approach for the long-term tests; for the maturities of one and five years, the forward rate biasedness is measured in exchange rate terms. It is simply a graphical depiction of the forecast error between a forward rate and the exchange rate it intended to estimate. The potential for a model misspecification, time series issues or the shown low volatility of the forward premium do not cause statistical interference for the described, simplified, inspection. On the contrary, if the behaviour of the forward premium is as highly stabile as it is assumed to be given the existing findings, the forward rate biasedness and time horizon effect will be facile and productive to analyse graphically.

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3

Hypotheses

The hypotheses to be tested are presented below followed by a clarifying commentary. These are employed for the data and models explained in the following chapter. There are four hypotheses set for this study. The first two investigate the unbiased forward rate hypothesis with a regression model that employs short-term data, ranging from one to twelve months. The second two hypotheses study the UIP in extended horizons by comparing one and five year time horizons. The methodology for the latter two is a simplified graphical inspection of the difference between a forward rate and the future exchange rate, i.e. the forward prediction error. The aim is to allow for a more detailed discussion of the findings as well as to neglect issues with econometric modelling.

The unbiased forward rate hypothesis suggests, as is indicated by its title, that a forward rate agreed at time t for a period i is an unbiased predictor of the future exchange rate that realizes synchronously with the forward contract i.e. exchange rate at time t+i. If the statement is valid then the null hypothesis is accepted and the regression equation (𝑠𝑡+𝑖− 𝑠𝑡= 𝛼 + 𝛽 (𝑓𝑡𝑖 − 𝑠𝑡) + 𝜀𝑡+1) produces statistically significant coefficient estimates (𝛽 = 1) and (𝑎 = 0). The latter, (𝑎 = 0), is of less interest and is rarely discussed in related articles.

H1: Statistically significant 𝛽 = 1 and 𝑎 = 0 from Fama regression for forward rate with maturity

(i=1-, 3-, 6-, 12-months)

The null hypothesis is tested for the aforementioned time horizons separately with currencies exhibited in the following section. If the null is accepted for any maturity it implies that the forward quote in question consistently forecasts the future spot rate accurately. Even if this hypothesis would be rejected the beta estimate can give valuable information in comparison to vast existing literature. For instance, a negative coefficient estimate implies not only a strong bias but also a systematic tendency of an increase in forward premium to be followed by a decline in exchange and vice versa. The literature usually measures the extent of forward rate or interest rate differential bias with the magnitude and the sign of the beta. In practice, the greater the difference of the estimated beta coefficient from unity, which is proposed by the null hypothesis, the greater the bias.

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The second hypothesis tested assumes that the beta approaches unity when the time horizon is extended up to one year. Hence, it tests the time horizon effect of the uncovered interest rate parity that frequently has been found to produce promising results in the advanced economies (Snaith, Coakley and Kellard 2013; Lothian and Wu, 2011). Related studies focusing on emerging markets have found concurring results, although such studies are remarkably limited (Sarmidi and Norlida, 2011). Consequently, in line with existing studies the beta is estimated to approach unity, although, not necessarily reach it. A growing discrepancy from (𝛽 = 1), on the other hand, would be suggestive of escalating bias and a clearer rejection of the uncovered interest rate parity. The maturity is restricted to 12-months in this hypothesis. The subsequent horizons are not examined with regression for two reasons: The data overlap is concluded to distort findings excessively if multiple years would be measured on a monthly interval and because the descriptive examination of the longer time periods allows for more detailed discussion. As Snaith, Coakley and Kellard (2013) argue, the Newey-West regression is not a comprehensive response to the overlapping sample issue.

H3: Forward rate biasedness disappears at distant time horizons: from one to five years.

The third hypothesis is similar to the second one but it is formulated slightly different given the difference in methodology employed. When the time horizon is extended further from the 12-months to include five years, the methodology is changed from the Fama regression specification to graphical a depiction of forward prediction error or forward rate bias. Here, the bias is measured in exchange rate terms with the difference between the future exchange rate and a forward rate committed to in a previous period: (𝑓𝑡𝑖 − 𝑠𝑡+𝑖). This examination is analogous to the original Fama regression, (𝑠𝑡+𝑖 =

𝛼 + 𝛽 (𝑓𝑡𝑖) + 𝜀

𝑡+1), in that if the unbiasedness in this regression holds, then (𝛽 = 1) and (𝑎 = 0)

resulting in (𝑠𝑡+𝑖 = 𝑓𝑡𝑖) which implies a zero forward prediction error: (𝑓𝑡𝑖 − 𝑠𝑡+𝑖= 0). Hence, if the unbiasedness disappears along with time horizon or the bias was to decrease, the variable values of (𝑓𝑡𝑖 − 𝑠𝑡+𝑖) would approach zero.

The choice of utilizing a more simplified approach in terms of econometric complexity was a deliberate one to achieve additional objectives set for this study. The varying statistical issues related to regressing a potentially long-memory, low volatility, forward premium with a difference-stationary exchange rate may be neglected. Subsequently in this thesis, especially the low variance of the forward premium will be assumed somewhat impair the regression model. In addition, measuring the prediction error gives directly information on the profitability of the forward rates. The unique

Figure

Figure 1: Illustrating the research topic: USD/BRL rate and hypothetical forward rates
Figure 2 illustrates the foundation for the hypothesis 4. It plots the historical USD/BRL spot rate for  the sample period and two completely hypothetical forward curves are drawn
Table 1: FX market imperfections in sample countries and data set description
Table 2 reports the volume in the OTC foreign exchange for the sample currencies. The data is retrieved from the triennial  central  bank  survey  2013  issued  by  the  Bank  for  International  Settlements 22
+7

References

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